Triangle calculator VC

Please enter the coordinates of the three vertices


Obtuse scalene triangle.

Sides: a = 10.19880390272   b = 4.4722135955   c = 8.24662112512

Area: T = 18
Perimeter: p = 22.91663862334
Semiperimeter: s = 11.45881931167

Angle ∠ A = α = 102.5298807709° = 102°31'44″ = 1.78994652727 rad
Angle ∠ B = β = 25.34661759419° = 25°20'46″ = 0.4422374223 rad
Angle ∠ C = γ = 52.12550163489° = 52°7'30″ = 0.91097531579 rad

Height: ha = 3.53300904325
Height: hb = 8.0549844719
Height: hc = 4.36656412507

Median: ma = 4.24326406871
Median: mb = 9
Median: mc = 6.70882039325

Inradius: r = 1.57109283145
Circumradius: R = 5.22334041216

Vertex coordinates: A[-3; 6] B[5; 8] C[-5; 10]
Centroid: CG[-1; 8]
Coordinates of the circumscribed circle: U[0; 0]
Coordinates of the inscribed circle: I[3.31664042195; 1.57109283145]

Exterior(or external, outer) angles of the triangle:
∠ A' = α' = 77.47111922908° = 77°28'16″ = 1.78994652727 rad
∠ B' = β' = 154.6543824058° = 154°39'14″ = 0.4422374223 rad
∠ C' = γ' = 127.8754983651° = 127°52'30″ = 0.91097531579 rad

Calculate another triangle




How did we calculate this triangle?

1. We compute side a from coordinates using the Pythagorean theorem

a = | beta gamma | = | beta - gamma | ; ; a**2 = ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 ; ; a = sqrt{ ( beta _x- gamma _x)**2 + ( beta _y- gamma _y)**2 } ; ; a = sqrt{ (5-(-5))**2 + (8-10)**2 } ; ; a = sqrt{ 104 } = 10.2 ; ;

2. We compute side b from coordinates using the Pythagorean theorem

b = | alpha gamma | = | alpha - gamma | ; ; b**2 = ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 ; ; b = sqrt{ ( alpha _x- gamma _x)**2 + ( alpha _y- gamma _y)**2 } ; ; b = sqrt{ (-3-(-5))**2 + (6-10)**2 } ; ; b = sqrt{ 20 } = 4.47 ; ;

3. We compute side c from coordinates using the Pythagorean theorem

c = | alpha beta | = | alpha - beta | ; ; c**2 = ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 ; ; c = sqrt{ ( alpha _x- beta _x)**2 + ( alpha _y- beta _y)**2 } ; ; c = sqrt{ (-3-5)**2 + (6-8)**2 } ; ; c = sqrt{ 68 } = 8.25 ; ;


Now we know the lengths of all three sides of the triangle and the triangle is uniquely determined. Next we calculate another its characteristics - same procedure as calculation of the triangle from the known three sides SSS.

a = 10.2 ; ; b = 4.47 ; ; c = 8.25 ; ;

4. The triangle circumference is the sum of the lengths of its three sides

p = a+b+c = 10.2+4.47+8.25 = 22.92 ; ;

5. Semiperimeter of the triangle

s = fraction{ o }{ 2 } = fraction{ 22.92 }{ 2 } = 11.46 ; ;

6. The triangle area using Heron's formula

T = sqrt{ s(s-a)(s-b)(s-c) } ; ; T = sqrt{ 11.46 * (11.46-10.2)(11.46-4.47)(11.46-8.25) } ; ; T = sqrt{ 324 } = 18 ; ;

7. Calculate the heights of the triangle from its area.

T = fraction{ a h _a }{ 2 } ; ; h _a = fraction{ 2 T }{ a } = fraction{ 2 * 18 }{ 10.2 } = 3.53 ; ; h _b = fraction{ 2 T }{ b } = fraction{ 2 * 18 }{ 4.47 } = 8.05 ; ; h _c = fraction{ 2 T }{ c } = fraction{ 2 * 18 }{ 8.25 } = 4.37 ; ;

8. Calculation of the inner angles of the triangle using a Law of Cosines

a**2 = b**2+c**2 - 2bc cos( alpha ) ; ; alpha = arccos( fraction{ a**2-b**2-c**2 }{ 2bc } ) = arccos( fraction{ 10.2**2-4.47**2-8.25**2 }{ 2 * 4.47 * 8.25 } ) = 102° 31'44" ; ; beta = arccos( fraction{ b**2-a**2-c**2 }{ 2ac } ) = arccos( fraction{ 4.47**2-10.2**2-8.25**2 }{ 2 * 10.2 * 8.25 } ) = 25° 20'46" ; ; gamma = arccos( fraction{ c**2-a**2-b**2 }{ 2ba } ) = arccos( fraction{ 8.25**2-10.2**2-4.47**2 }{ 2 * 4.47 * 10.2 } ) = 52° 7'30" ; ;

9. Inradius

T = rs ; ; r = fraction{ T }{ s } = fraction{ 18 }{ 11.46 } = 1.57 ; ;

10. Circumradius

R = fraction{ a }{ 2 * sin( alpha ) } = fraction{ 10.2 }{ 2 * sin 102° 31'44" } = 5.22 ; ;




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